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This graduate-level text presents the fundamental physics of
solid-state lasers, including the basis of laser action and the
optical and electronic properties of laser materials. After an
overview of the topic, the first part begins with a review of
quantum mechanics and solid-state physics, spectroscopy, and
crystal field theory; it then treats the quantum theory of
radiation, the emission and absorption of radiation, and nonlinear
optics; concluding with discussions of lattice vibrations and
ion-ion interactions, and their effects on optical properties and
laser action. The second part treats specific solid-state laser
materials, the prototypical ruby and Nd-YAG systems being treated
in greatest detail; and the book concludes with a discussion of
novel and non-standard materials. Some knowledge of quantum
mechanics and solid-state physics is assumed, but the discussion is
as self-contained as possible, making this an excellent reference,
as well as useful for independent study.
The polar regions (the Arctic and Antarctic) have enjoyed
widespread public attention in recent years, as issues of
conservation, sustainability, resource speculation and geopolitical
manoeuvring have all garnered considerable international media
interest. This critical collection of new and original papers - the
first of its kind - offers a comprehensive exploration of these and
other topics, consolidating the emergent field of polar
geopolitics. The expert international contributors to this volume
offer a range of insightful comparative, interdisciplinary and
global perspectives on polar issues. Key topics discussed include
resource extraction, regime formation, knowledge construction,
border issues, governance and treaties, and indigenous livelihoods.
Contributions from scholars of history, geography, political
science, anthropology and international law make this a truly
comprehensive take on the current state and future prospects of
both the polar regions and polar geopolitics as a distinct
discipline. Students and professors of geopolitics, political
science and geography - especially those with an interest in the
polar regions - will find much of value in this book s concrete
expression of a new and fascinating field.
This book provides a comprehensive treatment of the two fundamental
aspects of a solid that determine its physical properties: lattice
structure and atomic vibrations (phonons). The elements of group
theory are extensively developed and used as a tool to show how the
symmetry of a solid and the vibrations of the atoms in the solid
lead to the physical properties of the material. The uses of
different types of spectroscopy techniques that elucidate the
lattice structure of a solid and the normal vibrational modes of
the atoms in the solid are described. The interaction of light with
solids (optical spectroscopy) is described in detail including how
lattice symmetry and phonons affect the spectral properties and how
spectral properties provide information about the material's
symmetry and normal modes of lattice vibrations. The effects of
point defects (doping) on the lattice symmetry and atomic
vibrations and thus the spectral properties are discussed and used
to show how material symmetry and lattice vibrations are critical
in determining the properties of solid state lasers.
This graduate-level text presents the fundamental physics of
solid-state lasers, including the basis of laser action and the
optical and electronic properties of laser materials. After an
overview of the topic, the first part begins with a review of
quantum mechanics and solid-state physics, spectroscopy, and
crystal field theory; it then treats the quantum theory of
radiation, the emission and absorption of radiation, and nonlinear
optics; concluding with discussions of lattice vibrations and
ion-ion interactions, and their effects on optical properties and
laser action. The second part treats specific solid-state laser
materials, the prototypical ruby and Nd-YAG systems being treated
in greatest detail; and the book concludes with a discussion of
novel and non-standard materials. Some knowledge of quantum
mechanics and solid-state physics is assumed, but the discussion is
as self-contained as possible, making this an excellent reference,
as well as useful for independent study.
Whydowelookatsomethingsandthinktheyarebeautifulwhileotherthingsdo
notappearestheticallypleasingtous?Thisisaquestionthathasalwaysinterested
mankind.
Oneanswerisgivenbythefollowingquotationfromanearlypresidentof
theCollegeofNewJersey(nowPrincetonUniversity):
"Beautyisfoundinimmaterialthingslikeproportionoruniformity...calledbyvariousnamesofregularity,order,uniformity,symmetry,
1 proportion,harmony,etc. "...JonathanEdwards
Symmetrynotonlyprovidesthenaturalharmonythatmakessomethingappear
beautifultous,butalsoisofgreatvaluetosciencebecauseitdictatesthephysical
traitsofmanyobjects.
Natureitselfseemstolovebeautysinceatomstendtoself? assemble into
shapes with speci?c symmetry and crystals grow in geometric
lattices. Inmanycases,ifweknowthesymmetryofsomethingwecanpredict
someofitsimportantpropertieswithouthavingtoresorttoexperimentationor
complicatedcalculations. One area where the concept of symmetry
plays an important role is that of crystalline solids. Crystals, by
their very nature, exhibit speci?c symmetries.
Crystallinematerialshavemanyimportantapplicationsindevicesbasedontheir
electronic,optical,thermal,magnetic,andmechanicalproperties.
Solidstatep-
sicistsandchemists,aswellasmaterialscientistsandengineers,havedeveloped
rigorousquantumtheoreticalmodelstodescribethesepropertiesandsophisticated
measurementtechniquestoverifythesemodels.
Manytimes,however,inscreeningmaterialsforanewapplicationitisuseful
to be able to quickly and easily determine if a speci?c material
will have the
appropriatepropertieswithoutmakingdetailedcalculationsorexperiments.
This canbedonebyanalyzingthesymmetrypropertiesofthematerial.
Themathema-
calformalismthathasbeendevelopedtoaccomplishthisiscalledgrouptheory.
Thesymmetrypropertiesofacrystalcanbedescribedbyagroupofmathematical
1 J.
Edwards,WorksofJonathanEdwards(BannerofTruthTrust,Edinburgh,1979) v
vi Preface operations.
Thenusingsimplegrouptheoryprocedures,thephysicalpropertiesof
thecrystalcanbedetermined.
Duringthe45yearsIhavebeeninvolvedinteachingandresearchinvarious
areasofsolidstatephysics,Ihavemadeextensiveuseoftheconceptsofgroup
theory.
YetIhavebeensurprisedathowlittleemphasisthistopicreceivesinany
formaleducationalcurriculum.
Generally,astudentstudyingsolidstatephysicsor
chemistrywillbeexposedtocrystalstructuresearlyinthesemesterandthenhave
nofurtherexposuretocrystalsymmetryuntilsomespecialtopicsuchasnonlinear
opticsisdiscussed.
Thisbookfocusesonthesymmetryofcrystalsandthedescr-
tionofthissymmetrythroughtheuseofgrouptheory.
Althoughspeci?cexamples are provided of using this formalism to
determine both the microscopic and
macroscopicpropertiesofmaterials,theemphasisisonthecomprehensive,per-
sivenatureofsymmetryinallareasofsolidstatescience.
Theintentofthebookistobeareferencesourceforthosedoingresearchor
teachinginsolidstatescienceandengineering,oratextforaspecialtycoursein
grouptheoryappliedtothepropertiesofcrystals. Tucson,AZ RichardC.
Powell June2010 Contents 1 SymmetryinSolids...1 1. 1 Symmetry...1
1. 2 CrystalStructures...4 1. 3 SymmetryinReciprocalSpace...15 1. 4
Problems...24 References...24 2 GroupTheory...25 2. 1
BasicConceptsofGroupTheory...27 2. 2 CharacterTables...31 2. 3
GroupTheoryExamples...40 2. 3. 1 C PointGroup...40 3v 2. 3. 2 O
PointGroup...45 h 2. 4 GroupTheoryinQuantumMechanics...47 2. 5
Problems...52 References...53 3 TensorPropertiesofCrystals...55 3.
1 First-RankMatterTensors...5 7 3. 2 Second-RankMatterTensors...62
3. 3 Third-RankMatterTensors...68 3. 4
Fourth-RankMatterTensors...73 3. 5 Problems...77 References...77 4
SymmetryPropertiesofPointDefectsinSolids...79 4. 1
EnergyLevelsofFreeIons...79 4. 2 CrystalFieldSymmetry...85 4. 3
EnergyLevelsofIonsinCrystals...87 vii viii Contents 4. 4
Example:d?Electrons...95 4. 5 Example:f-Electrons...100 4. 6
Problems...104 References...104 5
SymmetryandtheOpticalPropertiesofCrystals ...
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